The non-back tracking clustering method estimates the number of clusters in a network, based on the spectrum of the non-back tracking matrix \(B\) , that contains information about 2-hop directed walks in a network \(G\) , that are not closed [1]}. Given an undirected network \(G(\mathcal {N},\mathcal {L})\) , for each link \(i \sim j\)  between nodes \(i\)  and \(j\) , two directed links \((i \rightarrow j)\)  and \((j \rightarrow i)\)  are created. By transforming each link in \(G\)  into a bi-directional link pair, we compose in total \(2L\)  links. The \(2L\times 2L\)  non-back tracking matrix \(B\)  is defined as follows:
\(B_{(u \rightarrow v),(w \rightarrow z)} = {\left\lbrace \begin{array}{ll}1 & \text{if $v = w$ and $u\ne z$}\\0 & \text{otherwise},\end{array}\right.}\) 
